I don’t think we did a very good job teaching geometry. In 2001, after spending a few hours with John Conway there in Fine Hall, he asked me, “Why are you so hung up on the octahedron?” I answered, “Because nobody knows what is perfectly enclosed within it.” I continued, “…we don’t know its most simple interior parts. …we don’t know about its four hexagonal plates. …we fail to recognize its necessary relation with the tetrahedron. Shall I go on?”

Ten years later with a high school geometry class we went deep inside that tetrahedral-octahedral complex. In 45 base-2 notations going within, we were well within particle physics. Within another 67 notations we were within the Planck Scale. We went back out; and from the desktop, it was only 90 additional doublings and we were at the approximate age and size of the universe. We then discovered Kees Boeke’s base-10. It had no inherent geometry. It had no Planck scale doublings. It was an empty shell while we had the dynamics of cubic-close packing.